SPM 2022 Add Maths Paper 1, Question 9Probability Distribution

Solved on video in English and Bahasa Melayu · Form 5, Probability Distribution · 5:53 video

The question

(a)

9 (a) Diagram 5 shows a conversation between Nash and Cikgu Wong. Cikgu Wong: 'Nash, please collect the shoe sizes of your classmates.' Nash: 'Alright sir. I know that the data is a discrete random variable.' Is Nash's statement true? Give your justification.

(b)(i)

9 (b) In a shooting competition, Dev fires n shots and p is the probability that his shot hits the target whereas q is the probability of not hitting. The probability that his shots hit the target at most once is 11 times the probability of not hitting the target at all. (i) Show that n(1 − q) = 10q.

(b)(ii)

9 (b)(ii) Hence, or otherwise, find the value of p and of q if the mean is 6.

SPM 2022 Add Maths Paper 1, Question 9: the question as drawn in Eduly's video5:53

Part (a)

Step 1

A discrete random variable takes values that can be counted (countable values).

2 more steps, each with the reason for it, in the full solution

Final answer

True: shoe sizes are countable (discrete) values

Where students lose marks

Watch out: don't just list values like 5, 6, 7. Say clearly that shoe sizes are countable, so the data is discrete.

Part (b)(i)

7 more steps, each with the reason for it, in the full solution

Final answer

Shown: n(1 − q) = 10q

Where students lose marks

Watch out: show the working in full. Write nC0 = 1 clearly when you substitute into the binomial formula.

Part (b)(ii)

5 more steps, each with the reason for it, in the full solution

Final answer

p = 2/5, q = 3/5

Where students lose marks

Watch out: give p and q in lowest terms, so write 2/5, not 4/10.

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